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#12 by N. J. A. Sloane at Thu Feb 07 12:52:15 EST 2019
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#11 by N. J. A. Sloane at Thu Feb 07 12:52:13 EST 2019
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Conjectures_Colin Barker_'s conjectures below are true.
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(End)) [These are true - see Comments]
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proposed
editing
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#10 by Charlie Neder at Wed Feb 06 21:59:15 EST 2019
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#9 by Charlie Neder at Wed Feb 06 21:59:11 EST 2019
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From Charlie Neder, Feb 06 2019: (Start)
Conjectures below are true.
From _Charlie Neder_, Feb 06 2019: (Start)Conjectures below are true.Proof: A267181(ka,kb) = A267181(a,b) since both operations preserve the greatest common factor of the two coordinates, so A267181(2k,2) = A267181(k,1) = k for k > 1, the second conjecture. For odd coordinates, we have the forced chain (2k+1,2) -> (2,2k+1) -> (2,2k-1) -> ... -> (2,1) -> (1,2) -> (1,1) with k+3 operations, the third conjecture. The rest follow from combining these. (End)
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#8 by Charlie Neder at Wed Feb 06 21:58:03 EST 2019
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From Charlie Neder, Feb 06 2019: (Start)Conjectures below are true.Proof: A267181(ka,kb) = A267181(a,b) since both operations preserve the greatest common factor of the two coordinates, so A267181(2k,2) = A267181(k,1) = k, the second conjecture. For odd coordinates, we have the forced chain (2k+1,2) -> (2,2k+1) -> (2,2k-1) -> ... -> (2,1) -> (1,2) -> (1,1) with k+3 operations, the third conjecture. The rest follow from combining these. (End)
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approved
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#7 by Michel Marcus at Fri Jan 29 10:51:21 EST 2016
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#6 by Joerg Arndt at Fri Jan 29 10:39:41 EST 2016
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#5 by Colin Barker at Fri Jan 29 09:49:59 EST 2016
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#4 by Colin Barker at Fri Jan 29 09:49:44 EST 2016
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Conjectures from Colin Barker, Jan 29 2016: (Start)
a(n) = (1-5*(-1)^n+2*n)/4 for n>0.
a(n) = (n-2)/2 for n>0 and even.
a(n) = (n+3)/2 for n odd.
a(n) = a(n-1)+a(n-2)-a(n-3) for n>3.
G.f.: (1+x-3*x^2+2*x^3) / ((1-x)^2*(1+x)).
(End)
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approved
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#3 by N. J. A. Sloane at Sun Jan 17 07:54:10 EST 2016
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